The present invention relates generally to correction, over a range of signal frequencies, of mismatch between in-phase “I” signals and quadrature-phase “Q” signals of an “IQ signal pair”. More particularly, the invention relates to circuitry and a method for correcting arbitrary mismatches, i.e., “IQ mismatches”, between an in-phase signal path or “I path” and a quadrature-phase signal path or “Q path” through which the IQ signal pair propagates.
IQ mismatch is the primary reason for the well-known infeasibility of building multicarrier radio receivers with zero IF (intermediate frequency). Zero IF receivers also are known as “direct conversion receivers”. The known IQ mismatch correction algorithms do not function properly for frequency-dependent IQ mismatches. However, it would be very desirable to have a practical system capable of estimating and correcting for arbitrary mismatches between an I path and a Q path of an IQ signal pair, especially without use of a calibration signal as is required by some existing IQ mismatch correction algorithms, because it is infeasible to add calibration tones at multiple frequencies to determine the mismatch across the multiple frequencies.
IQ mismatch also is a concern in other systems that employ quadrature mixing such as superheterdyne receivers employing IQ techniques for image rejection. For example, IQ systems are used in digital pre-distortion systems for improving PA (power amplifier) linearity.
Referring to FIG. 1, a conventional zero IF receiver 1 includes a low noise amplifier (LNA) 2 which amplifies an RF input signal RFIN and applies the amplified result to the input of a saw filter 3. The output of saw filter 3 is applied to both one input of a mixer 5A and one input of a mixer 5B. The other input of mixer 5A is coupled to receive an in-phase signal generated on conductor 9A by a phase shifting circuit 9. The other input of mixer 5B is coupled to receive a quadrature-phase signal generated on conductor 9B by phase shifting circuit 9. A local oscillator 7 generates a signal that is applied to the input of a buffer 8, the output of which is applied to the input of phase shifter 9. The quadrature-phase signal generated on conductor 9B is shifted in phase by 90° with respect to the in-phase signal on conductor 9A.
The output of mixer 5A is applied to the input of an adjustable gain amplifier 10A, the output of which is applied to the input of a LPF (low pass filter) 11A. The output of LPF 11A is applied to the input of a buffer 12A, the output of which is applied by means of a conductor 13A to the input of an ADC 14A. The digital output IOUT of ADC 14A is generated on a bus 15A. Similarly, the output of mixer 5B is applied to the input of an amplifier 10B, the output of which is applied to the input of a LPF 11B. The output of LPF 11B is applied to the input of a buffer 12B, the output of which is applied by means of a conductor 13B to the input of an ADC 14B. The digital output QOUT of ADC 14B is generated on a bus 15B. The signals IOUT and QOUT constitute an IQ signal pair.
The signal path including mixer 5A, amplifier 10A, LPF 11A, buffer 12A, and ADC 14A is referred to as an “in-phase path” or “I path” because mixer 5A receives the in-phase signal 9A generated by phase shifter 9. The signal path including mixer 5B, amplifier 10B, LPF 11B, buffer 12B, and ADC 14B is referred to as a “quadrature-phase path” or “Q path” because mixer 5B receives a quadrature-phase signal (shifted by 90°) generated on conductor 9B by phase shifter 9.
The correction equations for an IQ signal pair are as follows:Rfin=A cos [(ωc+ωm)t]+B cos [(ωc−ωm)t],  Eq. (1)where A is the message signal located at ωc+ωm and B is the message signal located at ωc−ωm, as shown in the upper spectrum plot in FIG. 2. After being mixed with a local oscillator output signal centered at ωc, both of message signals A and B would be located at ωm, as shown in the spectrum plots of the in-phase signal IOUT and the quadrature-phase signal QOUT in FIG. 2.
                              I          OUT                =                  LPF          (                                    cos              ⁡                              (                                                      ω                    c                                    ⁢                  t                                )                                      ⁢                          (                                                                    A                    ⁢                                                                                  ⁢                    cos                    ⁢                                          {                                              (                                                                              ω                            c                                                    +                                                      ω                            m                                                                          )                                            }                                                        +                                      B                    ⁢                                                                                  ⁢                                          cos                      ⁡                                              [                                                                              (                                                                                          ω                                c                                                            -                                                              ω                                m                                                                                      )                                                    ⁢                          t                                                ]                                                                                            ;                                                                        Eq        .                                  ⁢                  (          2          )                                                              I            ADC_OUT                    =                                                    A                2                            ⁢                              cos                ⁡                                  (                                                            ω                      m                                        ⁢                    nTs                                    )                                                      +                                          B                2                            ⁢                              cos                ⁡                                  (                                                            ω                      m                                        ⁢                    nTs                                    )                                                                    ,                            Eq        .                                  ⁢                  (          3          )                                                  Q          OUT                =                  LPF          (                                    sin              ⁡                              (                                                      ω                    c                                    ⁢                  t                                )                                      ⁢                          (                                                                    A                    ⁢                                                                                  ⁢                    cos                    ⁢                                          {                                              (                                                                              ω                            c                                                    +                                                      ω                            m                                                                          )                                            }                                                        +                                      B                    ⁢                                                                                  ⁢                                          cos                      ⁡                                              [                                                                              (                                                                                          ω                                c                                                            -                                                              ω                                m                                                                                      )                                                    ⁢                          t                                                ]                                                                                            ,                                                                  ⁢                and                                                                        Eq        .                                  ⁢                  (          4          )                                                  Q          ADC_OUT                =                                            B              2                        ⁢                          sin              ⁡                              (                                                      ω                    m                                    ⁢                  nTs                                )                                              +                                    A              2                        ⁢                                          sin                ⁡                                  (                                                            ω                      m                                        ⁢                    nTs                                    )                                            .                                                          Eq        .                                  ⁢                  (          5          )                    Message signals A and B can be separated as indicated in Equations 6 and 7, wherein the j operator imparts a phase shift of 90°.IADC—OUT+jQADC—out=A cos(ωmnTs);  Eq. (6)IADC—OUT−jQADC—OUT=B cos(ωmnTs).  Eq. (7)
FIG. 2 shows the spectrum of the RF input signal RFIN, the demodulated in-phase signal IOUT, and the demodulated quadrature-phase signal QOUT shown in FIG. 1. In the input spectrum shown in FIG. 2, there are two signals, ωc+ωm and ωc−ωm . ωc is the frequency of the carrier signal of the input signal RFIN. ωm is the frequency of the modulation signal, which is the signal of interest. When two RF signals having a carrier frequency ωc and a modulation frequency or signal frequency ωm, respectively, are multiplied or mixed, two signal components are generated, one of which has a frequency ωc+ωm, as shown in FIG. 2. The other signal component has a frequency ωc−ωm.
In the foregoing equations, the message signal or amplitude signal A corresponds to positive frequencies in the frequency domain spectrum of FIG. 2 and the signal B represents the negative frequencies therein. The mixing or demodulation of a positive frequency signal of magnitude A and a negative frequency signal of magnitude B appears in the frequency spectrum of the two signals on the horizontal axes in FIG. 2. The in-phase component of the positive frequency may be represented by the vector 27 in FIG. 3. The in-phase component IOUT appears along the x axis and the quadrature-phase component QOUT appears along the y axis in the vector diagrams. It can be seen that the signal Iresultant has a positive frequency and that the quadrature component 26,27 is rotated 90° in the clockwise direction, and for a negative frequency signal the quadrature component 26,27 rotates 90° in the counterclockwise direction. In this case, only the positive frequencies are of interest. Therefore, the positive frequency signal A is of interest, and the negative frequency signal B is to be completely canceled. Rotating the Q vectors 26,27 counterclockwise by 90° is accomplished by performing a “jQ” operation, wherein the B portion 26 rotates counterclockwise to the left as a result of the I+jQ rotation and completely cancels out the B/2 portion of vector 25. At the same time, vector 27 also rotates counterclockwise and adds its value A/2 to 2 the A/2 portion of vector 25 to form the resultant vector A=A/2+A/2.
The main components of IQ mismatch (i.e., mismatch between the in-phase and quadrature-phase paths of the IQ signal pair) include gain error mismatches between the ADCs, mixers, and amplifiers, phase deviation from 90° for the mixer in the Q path, mismatches in the pole frequencies of the LPFs (low pass filters), mismatches at the instants of time at which sampling occurs, and mismatches in the bandwidths of the ADCs. Such mismatches may cause generation of image tones. Mismatches in the instants of sampling and in the bandwidths of the two ADCs cause phase shift errors. For example, if the instant of sampling in the Q path is not exactly the same as the instant of the corresponding sampling in the I path, this causes a phase shift mismatch which may be problematic.
The most relevant prior art directed to correcting IQ mismatch is believed to include the following US patents. U.S. Pat. No. 6,330,290, entitled “Digital I/Q Imbalance Compensation”, issued Dec. 11, 2001, discloses single tap estimation and correction of IQ mismatch using test tone generation. U.S. Pat. No. 6,785,529 entitled “System and Method for I-Q Mismatch Compensation in a Low IF or Zero IF Receiver”, issued Aug. 31, 2004, discloses a correction scheme that applies a correction factor to at least one of the I and Q signals to correct for gain and/or phase errors. U.S. Pat. No. 5,872,538 entitled “Frequency Domain Correction of I/Q Imbalance” issued Feb. 16, 1999, discloses a technique based on use of a fast Fourier transform (FFT). U.S. Pat. No. 6,340,883 entitled “Wide Band IQ Splitting Apparatus and Calibration Method Therefor with Balanced Amplitude and Phase between I and Q”, issued Jan. 22, 2002, discloses a general technique for providing a calibration tone at multiple frequencies.
U.S. Pat. No. 7,177,372 entitled “Method and Apparatus to Remove Effects of I-Q Imbalances of Quadrature Modulators and the Modulators in a Multi-Carrier System”, issued Feb. 13, 2007, discloses splitting the input signal into individual signals and correction of IQ mismatch by adding portion of the image band into the band of interest. This reference is believed to be the closest prior art.
A known technique for single tap IQ mismatch estimation and correction is represented by the following equations:I=A cos(ωmnTs);  Eq. (8)Q=A(1−Δ)sin(ωmnTs+φ),  Eq. (9)where Δ represents gain mismatch between the I and Q paths and φ represents phase mismatch between the I and Q paths. Δ and φ may be estimated using Equations 10 and 11:ΣI2−ΣQ2=A2Δ;  Eq. (10)ΣIQ=A2 sin(φ).  Eq. (11)Based on Equations 8-11, it can be shown thatQout(DCcorrected)=(1Δ)Q+βI.  Eq. (12)where Δ and φ are assumed to be constant over the entire band of interest. Correction of the IQ mismatch using Equation 12 at a single frequency is referred to as “single tap correction”. In Equation 12 the gain mismatch estimate Δ corrects for gain mismatch, and the phase mismatch estimate φ corrects for the phase mismatch.
Equation 12 indicates a conventional way for single-tap imbalance estimation and correction algorithm circuit 32 to achieve single tap estimation and correction of the gain term of the IQ mismatch if Δ and φ are constant over the frequency band of interest. To correct for the gain mismatch in Equation 12, the signal QOUT is multiplied by a fraction (1+Δ), and the term β of the term βI is adjusted so as to make Δ equal to zero. That is, the gain Δ of the Q path is increased or decreased slightly so as to correct a mismatch in the Q path.
The vector or phasor analysis previously indicated in FIG. 3 indicates the conventional way for single-tap imbalance estimation and correction algorithm circuit 32 to correct for the phase mismatch φ. For the circuit condition represented by the vectors in FIG. 3, the I path and the Q path signals should be exactly 90° out of phase, and in effect, the vectors indicated are rotated so as to bring the I path signal and the Q path signal back to being exactly 90° out of phase.
FIG. 4A illustrates an implementation of a conventional single-tap IQ imbalance estimation and correction system which is a common single-tap prior art system that does not included any frequency dependent estimation/correction, pictorially illustrates a basic way of implementing Equation 12. β is an estimate of the phase mismatch, and Δ is an estimate of the gain mismatch. Blocks 21-1 and 21-6 represent the sources of the in-phase signal I and the quadrature-phase signal I, respectively. To obtain a value of the phase mismatch estimate φ, a summation ΣIQ is performed in block 21-2, using Equation 11. β is multiplied by I in block 21-4 and then is added in block 21-7 to Q. The value of Δ is obtained from Equation 10, using blocks 21-11 and 21-10 to obtain A2. Blocks 21-3, 21-9, and 21-11 generate ΣI2−ΣQ2 of equation 10, and that quantity needs to be divided by A2 to obtain Δ. Block 21-10 performs that division to generate Δ, which then is multiplied by Q, aunt block 21-8 generates the corrected quadrature -phase signal on conductor 15B.
The main drawback of a single tap correction is the inability to estimate and correct frequency dependent mismatches. Mismatches in the low pass filters in the in-phase path and the quadrature-phase path result in frequency dependent gain and delay mismatches. A single tap correction will fail to correct such mismatches.
Well known“multi-tap correction” techniques have been utilized for correcting mismatches of phase and amplitude that are variable across a frequency range of interest. The prior multi-tap correction technique splits the input spectrum into multiple channels and corrects each channel (but does not combine the split and corrected spectrum to provide the original full spectrum as described herein later). The known multi-tap correction techniques are not feasible when the channel count in a spectrum is large.
Difficulties associated with IQ mismatch are a primary reason for the infeasibility of building multicarrier radio receivers with zero IF (i.e., zero intermediate frequency). The existing mismatch correction algorithms do not work with frequency-dependent IQ mismatch.
Thus, there is an unmet need for a practical system and technique for determining the IQ gain mismatch and phase mismatch that vary significantly across a frequency range of interest.
There also is an unmet need for a practical way of determining the relation between the IQ gain and phase mismatches and filter coefficients h[N] at each frequency.